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Noise Figure
Measurement Accuracy
The Y-Factor Method
Application Note 57-2
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Table of contents
1 Introduction.....................................................................................................................................................4
2 Noise figure measurement...........................................................................................................................5
2.1 Fundamentals ..............................................................................................................................................5
2.1.1 What is noise figure? ..........................................................................................................................5
2.1.2 What is noise temperature? ..............................................................................................................6
2.1.2.1 Thermal noise power.............................................................................................................6
2.1.2.2 Noise temperature..................................................................................................................6
2.1.3 Noise figure in multi-stage systems.................................................................................................8
2.2 Y-factor measurement.................................................................................................................................8
2.2.1 Excess Noise Ratio (ENR)..................................................................................................................9
2.2.2 Y-factor .................................................................................................................................................9
2.2.3 Calibration .........................................................................................................................................10
2.2.4 Measurement with DUT...................................................................................................................10
2.2.5 Calculation of gain............................................................................................................................11
2.2.6 Second stage correction...................................................................................................................11
2.2.7 Summary ............................................................................................................................................11
3 Avoidable measurement errors .................................................................................................................12
3.1 Prevent interfering signals.......................................................................................................................12
3.2 Select the appropriate noise source.......................................................................................................13
3.2.1 Frequency coverage..........................................................................................................................13
3.2.2 Identity check....................................................................................................................................14
3.2.3 Use low ENR whenever possible ....................................................................................................14
3.2.4 When NOT to use low ENR..............................................................................................................14
3.2.5 Avoid adapters ..................................................................................................................................15
3.3 Use a preamplifier where necessary ......................................................................................................15
3.4 Minimize mismatch uncertainties ..........................................................................................................15
3.4.1 Use an isolator or attenuator pad..................................................................................................16
3.4.2 Minimize change in of noise source ...........................................................................................16
3.4.3 Measures of mismatch .....................................................................................................................16
3.4.3.1 VSWR: Voltage Standing Wave Ratio .................................................................................16
3.4.3.2 Reflection coefficient...........................................................................................................17
3.4.3.3 Return loss ............................................................................................................................17
3.4.3.4 S parameters.........................................................................................................................17
3.4.4 Mismatch-related errors ..................................................................................................................17
3.5 Use averaging to avoid display jitter ......................................................................................................18
3.6 Avoid non-linearity or unstable performance ......................................................................................20
3.6.1 Non-linearity......................................................................................................................................20
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3.6.2 Unstable performance......................................................................................................................20
3.7 Choose the appropriate measurement bandwidth ..............................................................................21
3.8 Account for frequency conversion..........................................................................................................22
3.8.1 Double sideband or single sideband measurement?...................................................................22
3.8.2 Estimating SSB noise figure from a DSB measurement.............................................................23
3.8.3 Local oscillator noise and leakage .................................................................................................24
3.8.4 What to check....................................................................................................................................25
3.9 Account for any other insertion losses..................................................................................................25
3.10 Correct for physical temperatures .....................................................................................................26
3.10.1 Noise source.......................................................................................................................................26
3.10.2 Noise generated in resistive losses ................................................................................................27
4 Loss and temperature corrections ...........................................................................................................27
4.1 Losses before the DUT..............................................................................................................................28
4.2 Losses after the DUT ................................................................................................................................28
4.3 Combined corrections ..............................................................................................................................28
4.4 Temperature of noise source ...................................................................................................................28
5 Calculating unavoidable uncertainties....................................................................................................29
5.1 Example system.........................................................................................................................................29
5.2 Example of uncertainty calculation .......................................................................................................30
5.3 Step by step ................................................................................................................................................31
5.4 Software tools ............................................................................................................................................33
5.4.1 RSS calculations................................................................................................................................34
5.4.2 TAG4 calculations.............................................................................................................................34
5.5 Effects of loss corrections on uncertainty ............................................................................................34
6 Practical implications ..................................................................................................................................36
6.1 Sources of uncertainty .............................................................................................................................36
6.2 Instrument noise figure and instrument errors...................................................................................37
6.3 Uncertainty versus DUT noise figure and gain ....................................................................................38
6.4 A possible solution re-define the DUT .............................................................................................38
6.5 How to use a preamplifier .......................................................................................................................39
6.5.1 When to use a preamplifier.............................................................................................................39
6.5.2 When not to use a preamplifier......................................................................................................39
6.5.3 How to calibrate the system............................................................................................................39
6.6 Solutions reduce ENR uncertainty......................................................................................................40
7 Checklist for improving measurement accuracy ...................................................................................41
Appendix A: Symbols and abbreviations.........................................................................................................42
Appendix B: Derivation of the RSS uncertainty equation ..........................................................................43
Appendix C: Connector care ..............................................................................................................................44
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1 IntroductionWhy is noise figure important?Noise figure is a key performance parameter in
many RF systems. A low noise figure provides
improved signal/noise ratio for analog receivers,
and reduces bit error rate in digital receivers.
As a parameter in a communications link budget,
a lower receiver noise figure allows smallerantennas or lower transmitter power for the
same system performance.
In a development laboratory, noise figure
measurements are essential to verify new
designs and support existing equipment.
In a production environment, low-noise receivers
can now be manufactured with minimal need
for adjustment. Even so, it is still necessary to
measure noise figure to demonstrate that the
product meets specifications.
Why is accuracy important?Accurate noise figure measurements have
significant financial benefits. For many products, a
guaranteed low noise figure commands a premium
price. This income can only be realized, however,
if every unit manufactured can be shown to meet
its specification.
Every measurement has limits of accuracy. If a
premium product has a maximum specified noise
figure of 2.0dB, and the measurement accuracy is
0.5dB, then only units that measure 1.5dB orlower are marketable. On the other hand, if the
accuracy is improved to 0.2dB, all products
measuring up to 1.8dB could be sold at the
premium price.
Customers need accurate noise figure measure-
ments to confirm they are getting the performance
they have paid for. Using the same example, an
accuracy of 0.5dB for measuring a product that a
manufacturer has specified as 2.0dB maximum
would require the acceptance of units measuring
as high as 2.5dB. An improved accuracy of 0.2dB
sets the acceptance limit at 2.2dB.
Speed of measurement is also an issue. High-value
products favor accuracy; high-volume products
favor speed. Due to the random nature of noise
and the statistical aspects of measuring it, there
is always a trade-off between speed and accuracy.
To optimize the trade-off, it is necessary to
eliminate all avoidable errors and to quantify
the uncertainties that remain.
This Application Note demonstrates how to
improve noise figure measurement accuracy byfollowing a three-stage process:
1. Avoid mistakes when making measurements
2. Minimize uncertainties wherever that is possible
3. Quantify the uncertainties that remain.
This Application Note covers the following topics:
Fundamentals of noise figure measurement
using the Y-factor method. (Chapter 2)
Noise figure mistakes to avoid (Chapter 3)
Measurement corrections to improve accuracy
(Chapter 4)
Calculation of the remaining uncertainties
including software tools (Chapter 5)
Other techniques that can reduce uncertainties
(Chapter 6)
Checklist for improving accuracy (Chapter 7).
Agilent Technologies Application Note 57-1,
Fundamentals of RF and Microwave Noise Figure
Measurements covers basic concepts behind
making noise figure measurements. These basic
concepts covered in Application Note 57-1 are
expanded on in Chapter 2 of this Application Note.
This Application Note is specific to instruments
that use the Y-factor method for noise figure meas-
urement. Various features of Agilent Technologies
products are mentioned as illustrative examples of
the newest generation of noise figure analyzersand noise sources. Other products, however, may
be used with the techniques discussed in this
document.
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2 Noise figure measurementThis chapter outlines the fundamental features
of the Y-factor measurement technique for noise
figure. Many instruments use the Y-factor
technique, including:
Agilent Technologies NFA Series noise figure
analyzers
Agilent Technologies PSA Series and ESA-E
spectrum analyzers with noise figure
measurement personality
Agilent Technologies X-Series signal analyzers
application with noise figure measurement
application
The equations developed in this chapter follow
the internal calculation route of the Agilent
Technologies NFA series noise figure analyzers.The calculation routes of other noise figure
instruments that use the Y-factor method are
inevitably similar.
This chapter departs from previous explanations
of noise figure calculations by making extensive
use of the noise temperature concept. Although
noise temperature may be less familiar, it gives a
truer picture of how the instruments actually work
and most important, how they apply corrections
to improve accuracy.
2.1 Fundamentals2.1.1 What is noise figure?
As explained in Agilent Technologies Application
Note 57-1, Fundamentals of RF and Microwave
Noise Figure Measurements, the fundamental
definition of noise figure F is the ratio of:
(signal/noise power ratio at the input of the device under test)
(signal/noise power ratio at the output of the device under test)
Or alternatively:
F = (Sin/Nin)/(Sout/Nout) (2-1)
Noise figure represents the degradation in
signal/noise ratio as the signal passes through a
device. Since all devices add a finite amount of
noise to the signal, F is always greater than 1.
Although the quantity F in equation (2-1) has
historically been called noise figure, that name
is now more commonly reserved for the quantityNF, expressed in dB:
NF = 10 log10F dB (2-2)
Agilent Technologies literature follows the
contemporary convention that refers to the ratio
F as noise factor, and uses noise figure to refer
only to the decibel quantity NF.
From the fundamental definition in equation (2-1)
a number of useful secondary equations for noise
figure can be derived. Equally fundamental is the
concept of noise temperature. Many of the internalcomputations of an automatic noise figure analyzer
are carried out in terms of noise temperature, so
it is important to understand this concept well
(see Section 2.1.2: What is noise temperature?).
Expressed in terms of noise temperature, the noise
factor F is given by:
F = 1 + Te/T0 (2-3)
Te is the effective (or equivalent) input noise
temperature of the device. Equation (2-3) also
introduces a reference temperature T0 which is
defined as 290K (16.8C, 62.2F). See Application
Note 57-1 for details of this derivation. The table
below shows a few comparisons between NF, F
and Te.
Noise Noise Noise
figure factor temperature
NF F Te
0dB 1 0K
(absolute zero)
1dB 1.26 75.1K
3dB 2.00 290K10dB 10 2,610K
20dB 100 28,710K
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2.1.2 What is noise temperature?Anyone concerned with noise measurements
should thoroughly understand the concepts of
noise figure, noise temperature and their
relationship.
Any electrical conductor contains electrons which
are somewhat free to move around more so in
good conductors, less so in near-insulators. Atnormal temperatures, electrons are in random
motion, although on average there is no net motion
unless an electromotive force is applied. This
random motion of electrons constitutes a
fluctuating alternating current that can be
detected as random noise.
At any temperature above absolute zero (where all
random motion stops) the thermal noise power
generated in a conductor is proportional to its
physical temperature on the absolute scale
(measured in kelvin, K). Thermal noise is spread
evenly over the electromagnetic spectrum (tobeyond 5,000 GHz), and therefore the noise
power detected by a receiver is proportional to
the bandwidth in which the noise is measured.
2.1.2.1 Thermal noise power
The basic relationship between thermal noise
power PN, temperature T and bandwidth is:
PN = kTB (2-4)
where PN is the noise power (watts)
k is Boltzmanns constant, 1.38 x 10-23 J/K
(joules per kelvin)B is the bandwidth (hertz)
For example, the thermal noise power generated
in a resistor at 290K (close to room temperature)
is 1.38 x 10-23 x 290 x B watts. This represents a
thermal noise power of 4.00 x 10-21W that is
generated in every hertz of the bandwidth B,
across the electromagnetic spectrum. PN is
independent of the ohmic value of the resistor.
Every circuit component, from near-perfect
conductors to near-perfect insulators, generates
thermal noise; however, only a tiny fraction of the
available noise power is normally detected. This isbecause the impedances of most individual circuit
components are grossly mismatched to typical
detection systems.
2.1.2.2 Noise temperature
If a 50 resistor at 290K is connected to theinput of a noise-free receiver with a 50 inputimpedance (Figure 2-1), the noise power input
to the receiver is:
PN = 1.38 x 10-23 x 290 x B watts (2-5)
Now imagine a device under test (DUT), such as anamplifier, connected between the 50 resistor andthe noise-free receiver (Figure 2-2). The noise at
the output of the DUT now has two components.
One is the amplified thermal noise from the input
resistor at 290K. The second is the noise generated
in the DUT itself. Note that the receiver cannot
distinguish these two components of noise. To the
receiver, the same output noise power density
could be measured from a noise-free DUT with its
input resistor heated to some higher temperature
(290 + Te). In effect the real DUT is modeled as a
noise-free equivalent device from which all internal
noise sources have been removed. This is combinedwith an additional thermal noise source Te at the
input. Te is the effective noise temperature of the
DUT (sometimes called the equivalent noise
temperature).
The advantage of the effective noise temperature
concept is that it forms a common basis for
measuring random electrical noise from any
source, from a GaAsFET to a galaxy. There are
many different types of electrical noise, and most
of them are not truly thermal in origin. However,
all types of random noise can be expressed as the
equivalent amount of thermal noise that would be
generated at a physical temperature Te. Generally
the word effective (or equivalent) is taken as
understood, and the normal term is simply
noise temperature.
Since the noise power PN is directly proportional
to temperature T (from equation 2-4), noise
temperatures can be added directly in the same
way as noise power provided that the bandwidth
B does not change.
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An example of this is calculating the noise
performance of a complete receiving system,
including the antenna. As a one-port device that
delivers noise power, an antenna has an effective
noise temperature TANT. If the receiver is designed
to operate from the source impedance of the
antenna (commonly 50 or 75) TANT can beadded directly to the receiver noise temperature
TRX to give the system noise temperature TSYS:
TSYS = TANT + TRX (2-6)
This analysis using noise temperatures provides
useful insights into the overall system perform-
ance, and can demonstrate whether TSYS is
dominated by TANT (which usually cannot be
changed) or by TRX (which often can be improved).
Note that such an analysis is not possible using
noise figure. This is because the fundamental
definition of noise figure cannot apply to a
one-port device such as an antenna.
The noise temperature concept also has to be used
in the correction of noise figure measurements for
resistive losses before or after the device under
test (Sections 4.1 and 4.2).
Noise measuring receiver
50T = 290K
Noise measuring receiver
50T = 290K
Same noise power
Noiseless DUT
Real DUT
Figure 2-1 A resistor at any temperature above absolute zero will
generate thermal noise.
Figure 2-2 Effective noise temperature is the additional temperature of
the resistor that would give the same output noise power density as a
noiseless DUT.
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2.1.3 Noise figure in multi-stage systemsThe noise figure definition outlined in Section
2.1.1 may be applied to individual components,
such as a single transistor, or to complete
multi-stage systems such as a receiver.1 The
overall noise figure of the system can be calculated
if the individual noise figures and gains of the
system components are known.
Figure 2-3 shows how the noise builds up in a
two-stage system. The input noise source is shown
as a resistor at the reference temperature T0
(290K). Each stage is characterized by its band-
width B, gain G and the noise Na that it adds.
The system noise factor F12 is then given by:
F12 = F1 + [(F2 - 1)/G1] (2-7)
(See Application Note 57-1 for the detailed derivation.)
Notice that the bandwidth B has canceled fromequation (2-7). This demonstrates one of the
advantages of the noise figure and noise tempera-
ture concept: it is independent of bandwidth.2
The quantity [(F2 -1)/G1] in equation (2-7) is often
called the second stage contribution. If the first
stage gain G1 is high, that will make the second
stage contribution small so that F12 will be mostly
determined by F1 alone. This is why a low-noise
receiver almost invariably begins with a low-noise,
high-gain RF amplifier or preamplifier.
Equation (2-7) can be re-written to find F1 if all the
other quantities are known:
F1 = F12 - [(F2 - 1)/G1] (2-8)
The same equation in terms of noise temperature is:
T1 = T12 - T2/G1 (2-9)
Equations (2-8) and (2-9) are the basis for most
automatic noise figure analyzers and similar
measurement instruments. The device under test
(DUT) is always Stage 1 and the instrumentation
connected to the DUT output is Stage 2
(Figure 2-4).
2.2 Y-factor measurementThe Y-factor technique is the most common
method of measuring the quantities required
by equations (2-8) or (2-9) to calculate the noisefactor F1 of the DUT.
This section begins by defining two important
quantities: the Excess Noise Ratio (ENR) of a
noise source, and the Y-factor itself.
Sections 2.2.3 through 2.2.7 then explain how the
complete Y-factor measurement is made.
Figure 2-3. How noise builds up in a two-stage system.
1. Note that noise figure of a receiving system can only extend to the receiver input it does not include the antenna. See What is noise
temperature? (2.1.2) for explanation.
2. Unless the bandwidth changes within the system being measured (see Section 3.7)
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2.2.1 Excess Noise Ratio (ENR)The Y-factor technique involves the use of a noise
source that has a pre-calibrated Excess Noise Ratio
(ENR). This is defined as:
ENR = (TSON - TSOFF) / T0 (2-10)
or more commonly in decibel terms as:
ENRdB = 10 log10 [(TSON - TSOFF) / T0] (2-11)
TSON and TSOFF are the noise temperatures of the
noise source in its ON and OFF states. T0 is the
reference temperature of 290K that appears in the
definition of noise figure (equation 2-3).
This definition of ENR supersedes an earlier
definition, ENR = [(TSON - T0) / T0], which
implicitly assumed that TSOFF was always 290K.
The new definition clarifies the fact that TSOFF
and T0 are usually two different temperatures.
Even so, the calibrated ENR of a noise source is
always referenced to TSOFF = T0 = 290K. Sections
3.10 and 4.4 explain how to correct for the
common situation where TSOFF is higher or lower
than the reference temperature.
2.2.2 Y-factorY-factor is a ratio of two noise power levels, one
measured with the noise source ON and the other
with the noise source OFF:
Y = NON/NOFF (2-12)
Because noise power is proportional to noise
temperature, it can be stated:
Y = TON/TOFF (2-13)
The instruments mentioned above are designed to
measure Y-factor by repeatedly pulsing the noise
source ON and OFF. NON and NOFF are therefore
measured several times, so that an averaged value
of Y can be computed.
Figure 2-4. Noise figure measurement uses a two-stage system.
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2.2.3 CalibrationThe complete Y-factor measurement of DUT noise
figure and gain consists of two steps, as shown in
Figure 2-5.
The first step is called calibration (Figure 2-5a)
and is done without the DUT in place. The noise
source is usually connected directly to the input
of the instrument.3
If the noise temperature of the instrument
(stage 2) is T2 then, according to equation (2-12),
the Y-factor measured by connecting the noise
source directly to its input will be:
Y2 = N2ON/ N2OFF = (TSON + T2) / (TSOFF + T2) (2-14)
or
T2 = (TSON - Y2TSOFF) / (Y2 - 1) (2-15)
TSOFF is the physical temperature of the noise
source, and TSON is computed from the noise
source ENRdB using equation (2-11).
At the end of calibration, the instrument stores
the measured values of N2ON and N2OFF, and the
computed values of Y2 and T2. It then normalizes
its noise figure and gain displays to 0 dB, ready
for the next step involving the DUT.
2.2.3.1 Alternatives to calibration
Measurements can be made without calibration for
convenience. Generally, this will result in substantially
higher errors unless the DUT gain exceeds 30 dB.
The PXA noise figure measurement application has
a feature called Internal Cal. This allows the con-
venience of not performing a calibration, while still
substantially reducing the errors due to instru-ment noise. Generally, Internal Cal will give results
that are as accurate as a full calibration when the
DUT gain is 15 dB or more.
2.2.4 Measurement with DUTNext, the DUT is inserted (Figure 2-5b) and the
Y-factor measurement is repeated. The system
now comprises the DUT (stage 1) followed by
the instrument (stage 2) as shown in Figure 2-4.
The combined Y-factor Y12 is given by:
Y12 = N12ON/ N12OFF (2-16)
Following equation (2-15), the combined noise
temperature T12 of the DUT followed by the
instrument is given by:
T12 = (TSON - Y12TSOFF) / (Y12 - 1) (2-17)
Figure 2-5. The Y-factor noise figure measurement requires two steps:
(a) Calibration, (b) Measurement of DUT.
(a) Calibration
(b) Measurement
Noise source
Noise source
DUT
3. The calibration step is comparable to the normalization step when using a network analyzer before the DUT is inserted, the instrument first measures itself.
Measurement reference plane
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2.2.5 Calculation of gainSince the instrument now has values for N12ON and
N12OFF as well as the previously stored values for
N2ON and N2OFF it can compute the gain of the DUT:
G1 = (N12ON - N12OFF)/ (N2ON - N2OFF) (2-18)
Usually the instrument displays G1 in dB:
G1,dB = 10 log10G1 dB (2-19)
2.2.6 Second stage correctionThe instrument has now measured T2, T12 and G1.
Equation (2-9) has determined that:
T1 = T12 - T2/G1 (2-9)
The instrument now has all the information it
needs to compute T1, the noise temperature of the
DUT, corrected for the noise contribution of the
instrument itself.
Most automatic (computing) noise figure instru-
ments can display the results in terms of either
noise temperature T (in K), noise factor F (ratio)
or noise figure NF (in dB). The conversions are
made using equations (2-1), (2-2) and (2-3).
2.2.7 SummaryThis section has described in some detail the
measurements and internal computations carried
out by an automatic noise figure instrument that
uses the Y-factor method. This information willhelp in understanding the information covered in
the next three chapters:
Avoidable measurement errors (Chapter 3)
Loss and temperature corrections (Chapter 4)
Calculating unavoidable uncertainties (Chapter 5).
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3 Avoidable measurement errorsThis chapter explains:
Common errors to avoid when making noise
figure measurements
Routine precautions to minimize common errors
Practical hints
3.1 Prevent interfering signalsAs explained in Chapter 2, all noise figure
instruments measure a sequence of different RF
noise power levels. Any RF interference, either
radiated or conducted, will masquerade as noise
power and affect measurement accuracy.
Interfering RF signals can cause errors of any
size in noise figure and gain. Small errors may
escape unnoticed unless an operator is alert to
the possibility of interference.
Figure 3-1 shows the kinds of stray signals that
could be coupled into the signal path and affect
the measurement. Fluorescent lights, nearby
instruments and computers, two-way radios,
cellular telephones, pocket pagers and local TV or
radio transmitters can all interfere with accurate
noise measurements.
The path by which RF interference enters the
measurement system can be either:
Direct radiation, with voltages and currents
being induced by the electrostatic, magnetic or
electromagnetic field.
Conduction through signal, power, and
control cables.
Measurements on receiver components are
especially vulnerable to interference from the
transmitters they are designed to receive. For
example, if testing a cellular telephone receiver,
check particularly for interference from cellular
phones and base stations nearby. A frequency-
swept measurement is more likely to reveal
interference than a single-frequency measurement.
This is because the sweep often shows clear
anomalies at frequencies where interference ispresent. The interference may also change between
sweeps, so that measurements seem to be unstable
at certain frequencies only. Once the possibility
of interference has been identified, a spectrum
analyzer or a receiver can be used to investigate
more closely.
Figure 3-1. Avoid these interference sources that can affect noise figure measurements.
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To avoid interference problems, check the
following items:
Use threaded connectors in the signal path
whenever possible. (Non-threaded connectors
such as BNC or SMB have lower contact forces
on the outer shield, which may affect shielding
integrity.)
Ensure that mating connectors are clean and not
worn or damaged. Ensure that readings remain
stable when lightly shaking the cables and
connectors.
Use double shielded coaxial cables (some regular
coaxial cables have inadequate shielding for
these sensitive measurements). Try to avoid
using flexible cables at the interface where the
signal levels are lowest. If the DUT has gain,
connect the noise source directly to its input. If
the DUT has loss, connect its output directly to
the input of the measurement instrument.
Use shielded GP-IB cables to prevent radiation
or pickup of interference from the control
network.
Avoid making measurements on an open PC
breadboard. Use shielding, especially if there is
a nearby transmitter that has any output
within the measurement bandwidth.
Relocate the whole setup to a screened room if
the DUT and measurement system cannot be
shielded adequately on an open bench. It may be
necessary to attenuate stray signals as much as
70 to 80 dB.
Skip over the frequencies of discrete interfering
signals when making a swept NF measurement,
if the instrumentation and the measurement
protocol allow.
Avoid interference from the instrument itself
by using a noise figure analyzer with low RF
emissions.4
3.2 Select the appropriate noise sourceNoise sources are available to cover frequencies up
to 50 GHz and beyond, with choices of waveguide
or co-axial connectors. Most commercial noise
sources are supplied with a calibration table of
ENR values at specific frequencies.
The ENR calibration uncertainties vary over the
frequency range of the noise source, and willcontribute to the overall uncertainty in the noise
figure measurement often almost dB-for-dB
(see Chapter 5).
For high quality noise sources this uncertainty is
about 0.1dB, which is adequate for most purposes.
Noise sources can be specially calibrated to reduce
this uncertainty. This is not a cost-effective option
until all other possibilities for reducing uncertainty
have been considered.
3.2.1 Frequency coverage Use a noise source whose calibration covers the
frequency of the measurement.
The ENR of a well designed noise source changes
only gradually with frequency, and there are no
marked resonances, so linear interpolation
between calibrated frequencies is acceptable.
If the DUT is a mixer or other frequency-converting
device, the noise source should preferably cover
both the input frequency and the output frequency
of the DUT. A full-featured noise figure analyzer
will select the correct ENR data for the calibrationand measurement steps.
If one noise source cannot cover both frequencies,
the calibration step and the DUT measurement
step must use two different noise sources. The
difference in ENR must be accounted for. Some
automatic noise figure instruments can make this
correction but may need to be told when the
noise source has been changed.5
4. Agilent Technologies has designed the NFA Series of instruments so that RF emissions from the instrument itself can have little or no impact on the NF
measurement. The instruments are also highly immune to radiated or conducted RF interference except, of course, through the INPUT port.
5. The latest generation of noise sources , identify themselves to the instrument automatically, and upload their own individual ENR table to the instrument.
These noise sources operate with noise figure analyzers such as the NFA Series and X-Series spectrum analyzers.
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3.2.2 Identity checkIf more than one noise source is available, check
that the noise figure instrument is using the
correct ENR calibration table.5
3.2.3 Use low ENR whenever possibleNoise sources are commonly available with
nominal ENR values of 15dB and 6dB.
Use a 6dB ENR noise source to measure noise
figures up to about 16-18dB, and particularly to
minimize measurement uncertainties if:
The DUT noise figure is very low; and/or
the gain of the device is especially sensitive to
changes in the noise source impedance.
A low ENR noise source has the following
advantages:
If the device noise figure is low enough to bemeasured with a 6dB ENR noise source, the
noise power levels inside the noise figure
instrument will be lower. This reduces potential
errors due to instrument non-linearity
(see Section 3.6).
The impedance match between the noise source
and the DUT changes slightly when the source is
switched between ON and OFF. The noise output
and gain of some active devices (especially
GaAsFETs) are particularly sensitive to changes
in input impedance. This can cause errors in
both gain and noise figure measurement. The6dB ENR noise sources contain a built-in
attenuator that both reduces the ENR and limits
the changes in reflection coefficient between ON
and OFF states. Section 3.4.2 gives more details.
The instruments own noise figure is a
significant contributor to the overall measure-
ment uncertainty (see Chapters 2 and 5). The
lower the instruments internal noise figure,
the lower the uncertainty. Many automatic
noise figure instruments will insert internal
attenuators to handle higher noise input levels.
This attenuation will increase the instrumentsnoise figure. With a low ENR noise source, the
instrument will use less internal attenuation,
which will minimize this part of the measure
ment uncertainty.
Avoid overdriving the instrument beyond its
calibrated input range when using a 6dB ENR
noise source with a DUT that has very high gain.
A noise figure instrument that is not auto-ranging
can be driven into non-linearity by a DUT with
very high gain. This results in the measurement
errors described in Section 3.6.1.
Auto-ranging noise figure instruments are less
vulnerable to this problem because they automati-
cally insert internal attenuators if necessary. A
minor problem is that a low ENR noise source
might not allow the instrument to self-calibrate on
all of its internal attenuation ranges. If the DUT
has more than about 40dB gain, the instrument
may have to use higher attenuation ranges that
have not been calibrated.6
In both cases, the solution is still to use the low
ENR noise source, but to insert a fixed attenuator
after the DUT to reduce its gain. This attenuator
must not be included in the calibration loop; it
must be accounted for separately (see Section 4.2
for details).
3.2.4 When NOT to use low ENRDo notuse a 6dB ENR noise source for
measurement of noise figures significantly
above 16dB. Use a 15dB ENR source instead.
When the DUT noise figure is high and the noise
source ENR is low, the difference in noise levelsbetween the noise source ON and OFF becomes
very small and difficult to measure accurately.
This affects the instrument uncertainty
(NFInstrument in Section 5.3, Step 4) in a way that isdifficult to quantify. Also, very long averaging
times are needed to prevent jitter from making a
significant contribution to the overall measuring
uncertainty (see Section 3.5).
There is no sharp limit on DUT noise figure where
uncertainty suddenly becomes excessive. Accuracy
deteriorates progressively with increasing
difference between the DUT noise figure andthe noise source ENR.
6. The Agilent Technologies NFA series noise figure analyzers indicate this condition on the display.
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A noise source is suitable for accurate measure-
ment of noise figures up to about (ENR + 10)dB,
with increasing care as this level is approached
or exceeded. Thus a 6dB ENR source is generally
capable of good accuracy in measuring noise
figures up to about 16dB, and a 15dB ENR
source up to about 25dB.
If the DUT noise figure is 15dB above the ENR, orhigher, measurement accuracy is likely to be poor.
3.2.5 Avoid adaptersThe calibrated ENR of a noise source is quoted at
its output connection plane. If it is necessary to
use adapters between the noise source and the
DUT, a correction must be applied for the adapter
losses at the input of the DUT (Section 4.1). Any
uncertainty in the value of this correction will
contribute dB-for-dB to the overall measurement
uncertainty. It is always preferable to obtain a
noise source with the correct connector to mate
directly to the DUT.
3.3 Use a preamplifier where necessaryThis recommendation is closely related to choosing
the appropriate noise source. It applies particularly
to spectrum analyzers that are used with a noise
figure measurement personality.7 This personality
can convert a spectrum analyzer into a highly
effective noise figure analyzer, except that the
instrument noise figure of a spectrum analyzer is
significantly higher than that of a modern purpose-
built noise figure analyzer. Therefore, if a spectrum
analyzer is being used to measure low noise figures
using a low ENR noise source, it will generally
require a low-noise preamplifier to minimize
measurement uncertainties.8
A preamplifier may also be needed with older
noise figure meters that have a relatively high
instrument noise figure, or with other instruments
that can be used to measure noise power level
(see Application Note 57-1 for more informationabout these alternative techniques).
A noise figure analyzer that has a low internal
noise figure will not require an external preampli-
fier unless the DUT has an unfavorable combina-
tion of low noise figure and low gain. Section 6.5
will explain how to calculate the uncertainties
with or without a preamplifier, and hence how
to decide whether the preamplifier is needed.
3.4 Minimize mismatch uncertaintiesMismatch at any interface plane will create
reflections of noise power in the measurement
path and the calibration path (as shown in
Figure 3-2). Mismatch uncertainties will combine
vectorially and will contribute to the total
measurement uncertainty.
The best measurement technique is to minimize
all avoidable mismatch uncertainties, and then
use the information in Chapter 5 to account for
the uncertainties that remain.
Figure 3-2. Example of mismatch effects.
7. For example, the Agilent Technologies ESA-E Series and PSA Series spectrum analyzers with noise figure measurement personality.
8. For example, the Agilent Technologies option 1DS for the PSA Series or ESA-E Series when working below 3GHz.
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3.4.1 Use an isolator or attenuator padAn isolator is a one-way device that transmits
incident RF power with only a small insertion loss,
but absorbs any reflected power in a matched load.
Placing an isolator between the noise source and
the DUT can prevent reflections from reaching the
noise source where they could reflect again and
combine with the incident signal. Isolators, however,
operate over restricted frequency ranges. A wide-band frequency-swept measurement may need to
be stopped several times to change isolators, and a
continuous frequency sweep will not be possible.
Also, each isolator has its own frequency-dependent
input/output mismatch and insertion loss.
Therefore each isolator must be accurately
characterized using a network analyzer, and
frequency-dependent corrections applied in the
noise figure calculation (see Section 4.1).9
Another method to reduce mismatch between the
noise source and the DUT is to insert a resistive
attenuator pad between the two. This has the effectof attenuating reflections each time they pass
through the pad. For example, a perfectly matched
10dB attenuator will have a return loss of 20dB for
reflected signals.10 Unlike an isolator, a resistive
attenuator has the advantage of broadband
response. The disadvantage is that an attenuator
reduces the ENR of the noise source (as seen by
the DUT) by its insertion loss. To avoid ENR
uncertainties, the insertion loss of the attenuator
must therefore be accurately characterized across
the required frequency range, and a correction
applied in the noise figure calculation
(see Section 4.1).9
A better alternative, where possible, is to use a low
ENR noise source which has a built-in attenuator
whose effects are already included in the ENR
calibration (see Section 3.2.3). In this case, no loss
correction is required.
3.4.2 Minimize change in of noise sourceSome low-noise devices (notably GaAsFETs) have a
particularly high input reflection coefficient. Even
a small change in the output reflection coefficient
of the noise source between its ON and OFFconditions can cause significant errors in the
measured noise figure. Even worse, if the input
circuit of a low noise amplifier is being adjusted
to the minimum noise figure, changes in noise
source reflection coefficient can result in a false
minimum. To minimize these effects, an attenuator
pad or isolator must be used between the noise
source and the DUT. Fortunately, low-noise devices
are best measured using a low ENR noise source,
which already contains a built-in attenuator.
No correction for the change in noise source
reflection coefficient is possible without extremely
detailed information about the effects of input
reflections on the noise and gain performance of
the DUT. Usually, the only workable strategy is to
minimize the changes.
3.4.3 Measures of mismatchThere are several ways to express how well an
RF impedance is matched to the system design
impedance (usually 50 but sometimes some otherresistive impedance such as 75). The fourcommon quantities used are VSWR, reflectioncoefficient, return loss and the S-parameters S11
or S22. RF engineers tend to use these terms
interchangeably, depending on the type of device
or the network property they wish to emphasize.11
3.4.3.1 VSWR: voltage standing wave ratio
This relates to the standing wave that is formed
on a transmission line by the interaction between
the forward and reflected travelling voltage waves.
VSWR is literally VMAX/ VMIN for the standing wave.
At suitable frequencies, VSWR can be measured
directly by a slotted-line probe in either a coaxialline or waveguide. Alternatively a bridge
or directional coupler can resolve the forward
and reflected waves on the line (VFWD and VREFL)
and then:
VSWR = (VFWD + VREFL) / (VFWD - VREFL) (3-1)
VSWR is ideally 1 on a matched line, and greater
than 1 in practice. VSWR is a scalar quantity
it describes the magnitude of a mismatch but
contains no information about the phase.
9. The Agilent Technologies analyzers with noise figure capability have a loss compensation facility to correct for losses between the noise source and the
input of the DUT.
10. See section 3.4.3: Measures of mismatch.
11. S-Parameter Design, Agilent Technologies Application Note 154, March 1990 (5952-1087). and S-Parameter Techniques for Faster, More Accurate
Network Design, Agilent Technologies Application Note 95-1, 1996 (5952-1130); also available as Agilent Interactive Application Note 95-1,
http://www.tm.agilent.com/data/static/eng/tmo/Notes/interactive/an-95-1/
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3.4.3.2 Reflection coefficient
Reflection coefficient (the Greek letter rho) isdefined simply as lVREFL/ VFWDl, so:
VSWR = (1 + ) / (1 - ) or (3-2)
= (VSWR - 1) / (VSWR +1) (3-3)
is a scalar quantity that is ideally zero on amatched line and greater than zero in practice.
The quantity (VREFL/ VFWD) is the complex reflec-
tion coefficient (the Greek capital letter gamma);it is a vector quantity with both magnitude and
associated phase angle.
3.4.3.3 Return loss
Return loss is the ratio in dB of forward and
reflected power:
RLdB = -10 log10(PREFL/ PFWD)
= -20 log10(VREFL/ VFWD) = -20 log10() (3-4)
The higher the return loss, the better the
impedance match. Return loss from an ideally
matched line is infinite. A return loss of 0dB
represents total reflection from a complete
mismatch. Return loss can either be a scalar
quantity or a vector quantity.
3.4.3.4 S-parameters
S (scattering) parameters are a method of
describing the behavior of incident and reflected
waves at the ports of a network. In a two-port
network, S11 is the input reflection coefficient andS22 is the output reflection coefficient (S21 is the
forward transfer parameter, and S12 describes
the reverse transfer). S-parameters are almost
invariably measured as vector quantities with both
magnitude and an associated phase angle, so S11
and S22 are complex reflection coefficients like .
3.4.4 Mismatch-related errorsInsertion loss can generally be divided into
two parts:
Dissipative (resistive) loss
Reflection (mismatch) loss.
In noise figure measurements, dissipative
mechanisms are recognized as a source of bothinsertion loss and thermal noise (Sections 4.1-4.3).
Reflection mechanisms do not generate thermal
noise, but they are a source of uncertainty. This is
because scalar measurements of insertion loss and
VSWR (or reflection coefficient) cannot predict
how the vector reflection coefficients will combine
when two imperfectly matched components are
connected.
One approach, taken in some network analyzers
that also have the capability of noise figure
measurement, is to measure the vector mismatches
and apply a correction. Unfortunately this is not afull correction because it overlooks an extremely
important fact: the mismatch changes the actual
noise figure of the DUT. To make a valid correction
for mismatch errors, it is necessary to know how
the DUT noise figure is affected by a range of
complex source and load impedances.
Neither a noise figure analyzer nor a network
analyzer with noise figure capability can generate
this information on its own. It requires a special-
ized automated test set that uses stub tuners to
present the DUT with a range of complex imped-
ances and incorporates a noise figure analyzer to
map the effects on gain and noise figure. As shown
in Figure 3-3, a test set can generate a Smith chart
showing circular contours of noise figure in the
complex impedance. It is important to note that
noise figure contours are almost never centered
on the 50 reference impedance at the center ofthe chart or on the conjugate match to the device
input impedance.
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Without the complete map of noise figure
contours which cannot be measured by a
network analyzer there is no way to be sure
that the correction for a vector impedance
mismatch will actually decrease the error of the
measurement. The error could even be increased.
It is invalid to attempt mismatch corrections
for noise figure measurements made using eithera noise figure analyzer or a network analyzer
with noise figure capability. Instead, impedance
mismatch should be minimized in the design of the
measurement, and any residual mismatch should
properly be treated as an uncertainty (Chapter 5).
Designers of modern noise figure analyzers have
concentrated on minimizing all other sources
of measurement uncertainty so that the total
uncertainty budget can almost always be reduced
to acceptably low values.
In uncommon cases where mismatch errors are
both unavoidable and significant, the only effectivesolution requires full mapping of noise figure
contours in the complex impedance plane using a
test set such as one available from ATN Microwave
(www.atnmicrowave.com).
3.5 Use averaging to avoid display jitterNoise is a result of a series of random independent
electrical events. In principle, the time required to
find the true mean noise level would be infinite.
Noise measurement captures a finite series of
these random events within the measurement
bandwidth, and therefore the results inherently
display random fluctuations or jitter. Averaging
many readings over an extended time period willreduce the displayed jitter, and bring the result
closer to the true long-term mean.
There is a trade-off between reduction of jitter
and the measurement time required. To obtain a
sufficiently accurate result, a suitable number of
readings must be averaged. Most computing noise
figure instruments have a facility for automatic
digital averaging over a selected number of inter-
nal readings (N), generally displaying a rolling
average over the last N readings.
Assuming that the noise being measured has a
gaussian probability distribution, averaging of N
readings will decrease the jitter by the square root
of N. As shown in the table below, by averaging 10
readings the jitter can be reduced to about 30% of
the value for a single reading (see Table 3-1).
Figure 3-3 The noise figure of most devices depends on the input impedance presented to the device. Without full knowledge of
the noise figure contours on a Smith chart, mismatch corrections can be uncertain and may introduce more error.
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As explained in Section 3.7, it is sometimes
necessary to make measurements in a reduced
bandwidth. In that case, the number of readings
averaged must be proportionally increased in order
to achieve the same level of jitter. For example, if
the bandwidth is reduced from 4MHz to 100kHz
(a factor of 40), readings must be averaged for 40
times as long to achieve the same level of jitter.
If speed is not the first priority (e.g. in an R&D
environment) the instrument should generally be
set to average sufficient readings to make the
residual jitter a minor component of the overall
measurement uncertainty (see Chapter 5). If speed
is a high priority (e.g. in a production environ-
ment) and the number of readings is low enough
to leave a significant uncertainty due to jitter, a
jitter contribution must be added to the overall
measurement uncertainty.
Jitter in the calibration step will add to the
uncertainty of all subsequent measurements.Therefore a long averaging time should be used
for calibration in order to reduce this source of
uncertainty to a negligible level. This is an
efficient use of time because it benefits all
subsequent measurements.
In frequency-sweep mode, two modes may be
available for updating the display while averaging
is taking place.12 Point averaging takes all the nec-
essary readings for each frequency before
averaging them and then moving on to the next
frequency. The average at each frequency is not
displayed until the measurement at that frequency
is complete. Trace averaging takes one reading at
each frequency across the whole frequency sweep,and then repeats the whole sweep as many times
as necessary, updating the display as it goes. Both
modes of averaging give the same result. Trace
averaging quickly displays a rough measurement
over the entire frequency range. Point averaging is
faster overall because the analyzer does not have
to change frequency after each reading.
Use trace averaging first. Watch a few sweeps
across the display and look for indications of RF
interference such as a spike in the response at a
single frequency, or even a small step in the
response. If there are no problems, change topoint averaging for faster measurements.
12. The Agilent Technologies NFA Series noise figure analyzers have both averaging modes. In the Agilent Technologies X-Series signal analyzers,
'point averaging' is controlled with the 'Avg Time/Pt' (average time per point) key.
Number
of readings
averaged % reduction
(N)
(N) in jitter % residual jitter
1 1 0 100
4 2 50.0 50.0
10 3.16 68.4 31.6
16 4 75.0 25.0
64 8 87.5 12.5
100 10 90.0 10.0
256 16 93.75 6.25
Table 3-1
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3.6 Avoid non-linearity or
unstable performanceAccurate noise figure measurements rely on the
linearity and stability of the entire measurement
system. This includes both the DUT and the noise
figure instrument itself.
3.6.1 Non-linearityAvoid operating either the DUT or the noisefigure instrument in a situation that would cause
non-linear behavior. In particular:
Do not attempt to measure devices that are
specifically designed to be non-linear, such as
logarithmic amplifiers or limiting amplifiers. The
techniques described in this Application Note
are not suitable for such devices. Similarly, do
not attempt to measure devices that need an
input signal in order to operate correctly
(e.g. systems that phase-lock to an input signal);
these require specialist techniques to measurenoise figure.
Avoid operating the DUT near its saturated
output power level where limiting occurs.
Accurate measurements require less than 0.05dB
gain difference between the ON and OFF states
of the noise source.
Disable any AGC circuits in the DUT, and take
manual control of the gain to establish the
required conditions for the measurement. Be
aware that AGC-controlled amplifiers may have a
limited linear range when operated without AGC.
Also, some systems control the gain by
techniques that can themselves introduce
non-linearity. If applying a temporary control
voltage, do not introduce hum or noise that will
modulate the gain.
Do not attempt to measure circuits that
self-oscillate or feed significant levels of local
oscillator leakage through to the noise figure
instrument; these will cause either RF inter-
ference or non-linearity. Even if far removed
from the measurement frequency, all signals of
this type should be regarded as RF interference
(see Section 3.1) and either suppressed within
the DUT or removed by an external filter.
Use a low ENR noise source whenever the
DUT noise figure is low enough to be measured
accurately with such a source (see Section 3.2).
The noise power levels inside the noise figure
instrument will be lower, which reduces
potential errors due to instrument non-linearity.
Insert in-line attenuation after a DUT with high
gain to avoid driving the noise figure instrumentbeyond its linear range. The instrument specifica-
tion will indicate the maximum total gain that
can be handled between the noise source and the
instruments input. If attenuation is needed after
the DUT, it must be accurately characterized
using a network analyzer and a correction must
be applied in the noise figure calculation
(Section 4.2).13
3.6.2 Unstable performanceTo avoid unstable or drifting performance, use
regulated power supplies for the DUT. Allow the
DUT and the noise figure instrument to warm up
and stabilize before starting measurements.
Consider keeping a reference device that can be
measured at the beginning of each day. This will
verify that the same result is obtained as on previous
days as well as confirm that the measurement
instrument is warmed up and has stabilized.
13. The Agilent Technologies analyzers with noise figure capability have a loss compensation facility to correct for losses between
the output of the DUT and the input port of the instrument. As already noted, there is a separate compensation facility for
losses between the noise source and the input of the DUT.
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Figure 3-4 A narrowband DUT can cause errors. Use a resolution bandwidth narrower than the bandwidth of the DUT.
3.7 Choose the appropriate
measurement bandwidthThe typical internal bandwidth of a noise figure
instrument is 34 MHz. Errors can arise if the DUT
contains filters that have a narrower bandwidth
than the instrument itself. During calibration the
instrument measures the total noise power within
its own internal bandwidth. However, during the
measurement the bandwidth is restricted by the
DUT (see Figure 3-4). This causes an error in the
DUT gain measurement, which affects the
correction for the instruments own noise
figure (Section 2.2.6).
The error becomes insignificant if the gain of
the DUT is high enough to be several orders of
magnitude greater than the ratio of the band-
widths during calibration and DUT measurement.
The DUT gain criterion is therefore:
[GDUT, dB] >>[10 log10(BCALIBRATION/ BMEASUREMENT)] (3-5)
If the DUT gain criterion cannot be met, choose a
resolution bandwidth that is significantly less than
the bandwidth of the DUT. Take into account the
possibility of relative drift between the two
passbands during the measurement. Both the
calibration and the measurement must use the
same bandwidth.
The modern full-featured NFA Series noise figure
analyzer, with digital signal processing, allows the
resolution bandwidth to be reduced from the IF
bandwidth of 4MHz down to 100kHz. Spectrum
and signal analyzers with the noise figure measure-
ment capability also have the facility to reduce the
IF bandwidth, often down to 1 Hz.
Alternatively, a suitably narrow bandpass filter can
be inserted between the DUT and the input of the
noise figure instrument. The instrument should
then be calibrated with the filter in place. The
insertion loss of the filter, however, will increase
the effective noise figure of the instrument. It may
be necessary to use a low-noise preamplifier to
avoid introducing new sources of uncertainty
(see Section 3.3).
Whichever technique is used for reducing band-width, it will always increase the averaging time
required to achieve the same low level of jitter
(see Section 3.5). This is because the number of
random noise events being averaged is reduced
in proportion to the bandwidth.14
14. For swept-frequency measurements with narrow bandwidth, the Agilent Technologies NFA Series noise figure analyzers can make blocks
of simultaneous measurements in adjacent channels that cover a total of almost 4MHz. The necessary averaging time remains the
same for each channel, but the simultaneous measurement feature can often reduce the time required for the complete frequency sweep.
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3.8 Account for frequency conversionIf the device under test includes a frequency
conversion between the input and the output
(Figure 3-5) the measurement takes place at a
different frequency from the calibration step
before the DUT was inserted (Section 2.2). In that
case, the following points will need to be carefully
considered.
3.8.1 Double sideband or single sideband
measurement?The noise source generates broadband noise. In a
double sideband measurement, noise input from
both the upper and the lower sideband (USB and
LSB) will be converted to the same intermediate
frequency (IF), as indicated in Figure 3-6. The
noise figure instrument will indicate an average of
the USB and LSB responses. If the DUT is designed
to accept input signals on both sidebands
(e.g. some radio astronomy receivers), then of
course a DSB measurement is required.
If the DUT is designed to respond to only one
sideband, the noise power input on the unwanted
sideband will usually be well suppressed by image
rejection filtering within the DUT (Figure 3-7a).
As a result the noise figure measurement will be of
a single sideband (SSB).
It is sometimes necessary to make an SSB noisefigure measurement on a DUT that contains no
image rejection filtering. In that case there are
two options. One is to insert an external image
rejection filter between the noise source and the
DUT (Figure 3-7b) and make a correction for the
loss in its passband (Section 4.1). The second
option is to make a DSB measurement and
estimate the SSB noise figure from that.
Figure 3-5. Frequency conversion measurement, where the DUT contains a mixer. The local oscillator (LO) may be either
internal or external to the DUT.
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Figure 3-7. Single-sideband noise
figure measurements: (a) DUT has
internal image rejection filtering. (b)
External filter between noise source
and DUT.
Figure 3-6. A double sideband
measurement responds to noise in both
sidebands (USB and LSB). Results may
be affected by variations in DUT, noisesource and instrument performance
with frequency.
3.8.2 Estimating SSB noise figure from
a DSB measurementDSB measurements are often seen as easier
because they avoid the added burden of image
rejection filter design and characterization. In the
simplest case, the SSB noise figure will be a factor
of 2 (3.0dB) lower than the DSB measurement.
This is only the case when both the ENR of the
noise source and the noise figure of the mixer arethe same at both the USB and LSB frequencies.
With many types of DUTs (e.g. broadband mixers)
the accuracy of this estimate can be improved by
lowering the IF at which the measurement is made.
This brings the upper and lower sidebands closer
together, and minimizes the effect of the frequency
difference (compare Figures 3-8 and 3-6).
Before attempting a definitive DSB noise figure
measurement that will be converted to SSB,
experiment with different IFs to see if frequency
variation errors are a problem. If the DSB noise
figure values change significantly with the choice
of IF, then SSB measurement is recommended.
One practical limit to lowering the IF is the
low-frequency limit of the noise figure instrument
(typically about 10MHz for instruments with
UHF coverage). Another practical limit is noise
sidebands in the local oscillator.
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3.8.3 Local oscillator noise and leakageNo oscillator produces a single, pure frequency.
In particular, the LO that is used in a noise figure
measurement with frequency conversion will
always generate noise sidebands on both sides of
the carrier frequency. Typically the noise sideband
level reduces with frequency offset from the carrier,
eventually reaching an almost constant noise floor
level that can be very broadband. As shown inFigure 3-9, high levels of the LO noise sidebands
or noise floor may contribute to the measured
noise power and may cause erroneous results.
The importance of LO noise entering the noise
figure instrument will depend on several factors:
The noise sideband level (measured in dBc/Hz,
i.e. relative to the carrier level and normalized to
a 1Hz bandwidth). The noise sideband power
density is a function of:
- the LO design, and many of its operatingparameters, especially level and frequency
- the IF, which is the offset between the
measurement frequency and the LO frequency;
the smaller this offset, generally the higher is
the noise sideband level
- the measurement bandwidth.
The broadband noise floor level.
The mixers LO to IF port isolation. A well-
balanced mixer may give a rejection of 30dB or
better for LO noise sidebands, but non-balanced
mixer configurations may have zero LO-IF isolation.
The noise figure and gain of the DUT.
As a general rule, the LO noise level at the IF
separation from the carrier should not exceed
-130dBm/Hz. More specifically:
[LO power level (dBm) - LO phase noise
suppression (dBc/Hz)]
should not exceed
[ -174 dBm/Hz + expected NF (dB) +
Gain of DUT (dB)] (3-6)
Another important factor is the level of LO
leakage through the DUT and into the noise figureinstrument. As noted in Sections 3.1 and 3.6, this
can cause errors by appearing as RF interference
and/or by overdriving the instrument into an
uncalibrated or non-linear region.
Figure 3-8. Reducing the IF for a DSB measurement can also reduce the effect of differences in noise figure (and/or ENR of noise source)
between the LSB and USB. Compare against Figure 3-5.
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Figure 3-9. In a frequency-converting system, noise sidebands from the LO can affect noise figure measurements.
3.8.4 What to checkWhen making measurements involving frequency
conversion, always check for the causes of error
described above. In particular:
Check whether the apparent DSB noise figurevaries with IF frequency.
Check for LO leakage, using a spectrumanalyzer at the output of the DUT. Applyfiltering if necessary.
Check for the effects of LO noise sidebands.
Apply all relevant corrections mentioned in thischapter for mismatch and losses ahead of andafter the DUT. Note that some of these correc-tions may also be frequency-dependent, andmay require close attention in a wideband
DSB measurement.
3.9 Account for any other insertion lossesPrevious sections mention several potential
sources of loss both reflective and resistive
(dissipative) before and after the DUT. As
a final check before making a definitive
measurement, ensure that all relevant losses
have been determined.
The calibration step before the measurement willestablish the measurement reference plane at the
output of the noise source (Figure 2-5a). This
automatically takes account of any losses between
the output of the DUT and the input of the noise
figure instrument. In effect, the losses are
absorbed into the instrument noise figure
NF2 as explained in Chapter 2.
When the DUT is inserted, the output of the noise
source should be connected as directly as possible
to the input of the DUT. All components that
were included in the calibration loop must still be
present between the output of the DUT and the
input of the noise figure instrument (Figure 3-10a).
If it is necessary to insert components between
the noise source and the input of the DUT (Figure
3-10b), these components must not be included in
the calibration loop. Their losses must be accounted
for separately as shown in Section 4.1.
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In many cases it will be necessary to replace the
DUT with an equivalent coaxial adapter, which is
thus included in the calibration loop. However, as
noted in Section 3.2, it is always preferable to use
a noise source that has a connector compatible
with the input of the DUT, so that the ENR
characterization data for the noise source apply
exactly at the measurement reference plane. If
it is necessary to add or remove an adapter wheninserting the DUT into the measurement loop,
arrange to do this at the output of the DUT.
If a preamplifier is needed as part of the measure-
ment system (Section 3.3) it should of course be
included in the calibration loop. In addition, the
input connector of the preamplifier should be
compatible with the connector of the noise source
in order to establish the correct reference plane.
Any necessary adapter should then be placed
between the output of the DUT and the input of
the preamplifier.
Chapter 4 explains how to correct noise figure
measurements for any further losses that have not
already been accounted for by the calibration step.
3.10 Correct for physical temperatures3.10.1 Noise sourceSection 2.2.1 defined the ENR of the noise source as:
ENR = (TSON - TSOFF) / T0 (2-7, 3-7)
ENRdB = 10 log10 ((TSON - TSOFF) / T0) (2-8, 3-8)
where TSOFF is the physical temperature of the
noise source (which still emits thermal noise in
its OFF condition) and T0 is the reference tempera-
ture of 290K. The ENR versus frequency tables that
characterize each individual noise source are refer-
enced to that temperature; it is assumed that
TSOFF = T0.
If TSOFF is not 290K, the ENR will not be correct.
This will lead to an error in noise figure as shown
in Figure 3-11. The physical temperature of the
noise source should then be measured and a
temperature correction applied. Most computingnoise figure instruments can correct for the actual
value of TSOFF, based on user input from the
keypad.15 (If the value entered is not correct, there
will be an error equal to that shown in Figure 3-11.)
For instruments that cannot calculate the correction
internally, Section 4.4 describes how to correct the
ENR by hand calculation.
Figure 3-10. Components that were in the calibration loop (a) must come after the DUT during the
measurement (b). Components between the noise source and the DUT input must not be included
in the calibration loop.
(a) Calibration
(b) Measurement
A DUTB
Use same components
as in calibration.
Components ahead
of DUT:
Do NOT include in
calibration loop. Account
for loss separately.
A
B
These components will
come AFTER the DUT.
15. The latest generation of noise sources designed for Agilent Technologies noise figure analyzers, such as the NFA Series a nd X-Series signal analyzers,
contain a temperature sensor and the correction is made automatically.
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3.10.2 Noise generated in resistive lossesAny components in the test setup that have
resistive losses (attenuators, cables etc.) willgenerate thermal noise in their own right. This
source of temperature-related error is often
overlooked. As well as allowing for the loss itself,
a complete correction needs to take account of the
noise generation in the components involved. This
in turn requires measurement of their physical
temperatures. Sections 4.1 and 4.2 show how to
make the corrections.
Corrections for physical temperature do not apply
to the DUT itself. Its physical temperature is
assumed to be part of the DUT test conditions, so
the measured noise figure and gain are applicable
at that physical temperature.
4 Loss and temperature
correctionsThis chapter explains how to make corrections
for the residual errors due to losses, either ahead
of or following the DUT. Closely related to this
is the correction for the physical temperature
of the noise source and the temperature of
lossy components.
The equations for the corrections are given in
terms of noise temperature because that is the
parameter most directly affected. For more
information on noise temperature, see Chapter 2.
All of the corrections described in this chapter are
frequency-dependent. Frequency-swept measure-
ments may need a table of corrections versus
frequency. A modern full-featured noise figure
analyzer has the capability to make the corrections
described in this chapter automatically if it is
supplied with frequency-dependent tables of
loss data.
27
Figure 3-11. Magnitude of error in noise figure measurement if TSOFF is not 290K. If the noise figure
instrument can correct for the actual value of TSOFF an equal error arises if the value input to the
instrument is not correct.
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4.1 Losses before the DUTThe reference plane for the ENR characterization
of the DUT is the output of the noise source
(Figure 2-5a). Any additional losses between that
reference plane and the input of the DUT must be
taken into consideration..
Section 2.2 derived the equation to calculate the
noise temperature T1 of the DUT, with a correctionfor the second stage contribution from the
instrument itself (T2/G1):
T1 = T12 - T2/G1 (2-6, 4-1)
For this loss correction, the input loss LIN needs
to be expressed as a ratio greater than 1, so that:
LIN = antilog10(LINdB/10) (4-2)
The correction for input loss changes the original
value of T1 to T1IN
. If the input loss ahead of theDUT is LIN (as a ratio greater than 1, not dB) then:
T1IN = [T1/LIN] - [(LIN - 1)TL/LIN] (4-3)
where T1 is the original displayed value of noise
temperature, and T1IN is the new value corrected
for input losses.
Equation (4-3) has two terms. The first represents
the direct effect of LIN upon T1. The second term is
the added noise contribution from thermal noise in
any resistive loss at a physical temperature TL. If
LIN is purely reflective (non-dissipative) in
character, omit the second term.
4.2 Losses after the DUTAs noted in Sections 3-9 and 3-10, correction for
losses after the DUT must only be applied to com-
ponents that had notbeen included in the calibra-
tion loop (Figure 3-10). For output losses the
correction is to T2, the noise temperature of the
instrument (as already modified by components
included in the calibration loop).
T2OUT = [T2/LOUT] - [(LOUT - 1)TL/LOUT] (4-4)
As in equation (4-2), LOUT is a ratio greater
than 1 and TL is the physical temperature of any
dissipative losses. Once again, if LOUT is purely
reflective (non-dissipative) in character, omit the
second term.
The modified value T2OUT is inserted into
equation (4-1) to calculate a new value of T1OUT,
which is the original value of T1 corrected for
output losses:
T1OUT = T12 - T2OUT/G1 (4-5)
4.3 Combined correctionsThe separate corrections for input and output
losses can of course be combined to give T1IN, OUT
which is the value of T1 after both corrections have
been applied:
T1IN, OUT = {T12 - [T2/ LOUT - (LOUT - 1) TL/ LOUT]
/G1 } / LIN - {(LIN - 1) TL/ LIN} (4-6)
A modern full-featured noise figure analyzer
has the capability to make these corrections
automatically if it is supplied with frequency-dependent tables of loss data.
4.4 Temperature of noise sourceContinuing from Section 3.10.1, if TSOFF is not
290K, the physical temperature of the noise source
should be measured and the following temperature
correction applied.
ENRCORR = ENRCAL + [(T0 - TSOFF) / T0] (4-7)
ENRdBCORR = 10 log10{ [antilog10[ENRdBCAL/ 10] +
[(T0 - TSOFF) / T0] } (4-8)
where
ENRCORR, ENRdBCORR are the corrected
ENR values (ratio or dB, respectively)
ENRCAL, ENRdBCAL are the original
calibrated ENR values (ratio or dB, respectively)
TSOFF is the actual physical temperature of the
noise source (K)
T0 is 290K.
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Figure 5-1 Model for uncertainty calculation.
5 Calculating unavoidable
uncertaintiesUnavoidable uncertainties are those that remain
after all the precautions in the previous chapters
have been taken. This chapter describes how the
unavoidable uncertainties contribute to the overall
measurement uncertainty.
Sections 5.1 through 5.3 give a detailed explanation
of uncertainty calculations for an example
system. Section 5.4 introduces a spreadsheet
calculator to automate the calculation.
5.1 Example systemFigure 5-1 shows the model that is used to illustrate
where uncertainties arise in noise figure measure-
ment and how to calculate them. The explanation
will use the same basic terms as Chapter 2.
The quantity to be measured is NF1, which the
instrument indicates as 3.00 dB. The sources of
uncertainly in this measurement are:
The uncertainty of NF2 as measured in the
calibration step (NF2 is 10dB for this example,
but is normally not displayed)
The uncertainty of NF12 as measured in the DUT
measurement step (which also is normally not
displayed)
The impedance mismatch between noise source
and instrument, in the calibration step
The impedance mismatch between noise source
and DUT, in the measurement step
The impedance mismatch between DUT and
instrument, in the measurement step
The uncertainty of the ENR of the noise source.
It is assumed that all other avoidable errors have
been minimized (see guidelines in Chapter 3). For
example, it is assumed that random jitter has been
reduced to a low level by averaging a sufficient
number of readings.
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5.2 Example of uncertainty calculationUncertainty calculations inevitably involve
statistical concepts. This simple example will use
RSS (root sum of squares) statistics which assume
that all sources of uncertainty are uncorrelated.
The equation that will be used to calculate the RSS
uncertainty of the noise figure measurement is:
where:
F1 is the noise factor of the DUT, as a ratio;
NF1 is the dB quantity
F2 is the noise factor of the noise figure
instrument, as a ratio; NF2 is the dB quantity
F12 is the noise factor of the complete system(DUT and instrument), as a ratio; NF12 is the
dB quantity.
G1 is the gain of the DUT, as a ratio; G1,dB is
the dB quantity
ENRdB is the Excess Noise Ratio of the noise
source, in dB
The terms are the associated uncertainties,always in dB.
S = 1 for a single-frequency measurement;
S = 0 for a measurement involving frequency
conversion.
For the derivation of this equation, see Appendix B.
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5.3 Step by stepThis section works through the uncertainty
calculation, step by step. This is usually done by
a computer. However, when learning about the
process it is valuable to explore the reasoning
behind each step.
Check boxes like this will mark each practical
operation. An automatic (computing) noisefigure instrument is assumed.
Step 1 Measurements Referring to the user documentation for a noise
figure instrument, calibrate the instrument (this
will zero the noise figure and gain displays).
Insert the DUT and measure the DUT gain (G1)
and corre